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GATE Engineering Mathematics: Complex Variables: Analytic functions, Cauchy integral formula, Taylor series, Laurent series, Residue theorem – Previous Year Questions

6 GATE previous year questions on Complex Variables: Analytic functions, Cauchy integral formula, Taylor series, Laurent series, Residue theorem (Engineering Mathematics, Electrical Engineering) with answers and explanations, from every paper.

  1. GATE 2017 EE Q12 (1 mark, Multiple choice) – For a complex number z, z i z2 + 1z3 + 2z - i(z2 + 2) is
  2. GATE 2016 EE Q15 (1 mark, Multiple choice) – The value of the integral C 2z + 5(z - 12)(z2 - 4z + 5) \, dz over the contour z = 1, taken in the anti-clockwise direction, would be
  3. GATE 2019 EE Q14 (1 mark, Multiple choice) – Which one of the following functions is analytic in the region z 1?
  4. GATE 2021 EE Q12 (1 mark, Multiple choice) – Let p(z)=z3+(1+j)z2+(2+j)z+3, where z is a complex number. Which one of the following is true?
  5. GATE 2024 EE Q30 (1 mark, Multiple select) – Which of the following complex functions is/are analytic on the complex plane?
  6. GATE 2025 EE Q55 (2 marks, Numerical answer) – Let C be a clockwise oriented closed curve in the complex plane defined by z =1. Further, let f(z)=jz be a complex function, where j=-1. Then,…